Exponentiated power Lindley power series class of distributions: Theory and applications |
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| Authors: | M. Alizadeh S.F. Bagheri E. Bahrami Samani S. Ghobadi S. Nadarajah |
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| Affiliation: | 1. Branch of Mazandaran, Statistical Center of Iran, Tehran, Iranalizadeh_mojtaba_san@yahoo.com;3. Department of Statistics, College of Basic Sciences, Yadegar-e-Imam Khomeini(RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran;4. Department of Statistics, Shahid Beheshti University, Tehran, Iran;5. Islamic Azad University, Qaemshahr Branch, Department of Mathematics, Qaemshahr, Iran;6. School of Mathematics, University of Manchester, United Kingdom |
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| Abstract: | ABSTRACTWe introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley power series (EPLPS) distribution. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the minimum lifetime value among all risks. The distribution exhibits a variety of bathtub-shaped hazard rate functions. It contains as particular cases several lifetime distributions. Various properties of the distribution are investigated including closed-form expressions for the density function, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Expressions for the Rényi and Shannon entropies are also given. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Finally, two data applications are given showing flexibility and potentiality of the EPLPS distribution. |
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| Keywords: | Hazard rate function Maximum likelihood estimation Model selection criteria Power series distributions Residual life function. |
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